Machine learning for time series forecasting: A statistical perspective

Abstract

Time series forecasting is a fundamental problem in many real-world applications, including healthcare, finance, and energy systems, where accurate predictions are essential for effective decision-making. Classical statistical models such as autoregressive integrated moving average (ARIMA) have been widely used due to their theoretical rigor and interpretability; however, their performance is often limited by assumptions of linearity, stationarity, and predefined error distributions. Recent advances in machine learning have introduced flexible, data-driven alternatives that demonstrate superior forecasting accuracy in complex environments. This study investigates the advantages of machine learning for time series forecasting from a statistical perspective using a controlled synthetic case study. A synthetic dataset representing daily hospital admissions is generated with trend, multiple seasonalities, and nonlinear dynamics to emulate real-world behavior. Forecasting performance of a classical ARIMA model is compared with a machine learning-based Random Forest regressor. Model evaluation is conducted using standard error metrics and residual diagnostics. The results show that the machine learning model consistently outperforms the statistical model, achieving lower prediction error and improved residual behavior. From a statistical viewpoint, this improvement is attributed to the ability of machine learning models to act as nonparametric estimators of conditional expectations while relaxing restrictive modeling assumptions. The findings highlight that machine learning complements rather than replaces traditional statistical approaches and provides a robust framework for forecasting complex time series data.